Another shooter fired five .357 lead bullets into his S&W Mod 27, but forgot to add powder, so four stuck in the bore and one only made it half-way out of the cylinder.
He brought it to me to see if I could take the bullets out, so this is what I did and think it should work on the Mosin barrel.
I unscrewed the barrel from the action, then, putting the barrel vertically in a vise, heated it with a torch just enough to melt the first bullet, then the second, etc. It worked very well and didn't damage the barrel because lead bullets melt at temperatures well below that which would damage the barrel.
In this case, I'd mount the barrel muzzle-upward and apply heat until the lead slug melted out and dropped into a pail. Once that's out, heat may loosen the wood by drying it out, but if not, and it's possible to insert a fired case, use one as a drill guide to drill out some of the wood, using a small pilot drill with the side flutes ground off or taped, so they don't touch the rifling.
That's my best advice, for what it's worth.